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While the new limited-edition flavor has brought chuckles from fans of the “Saturday Night Live” skit on which it’s based, some supermarket chains aren’t laughing and have been giving it a cold shoulder.

The flavor featuring fudge-covered rum balls has been absent from some grocery freezers since it was unveiled. The title was inspired by an innuendo-laced 1998 skit featuring Alec Baldwin as baker Pete Schweddy, who promises, “No one can resist my Schweddy balls.”

But apparently some grocery store chains can, and so can supporters and members of the One Million Moms group.

That Mississippi-based moms organization has been putting the heat on retailers to keep Schweddy Balls out of their freezers and encouraging parents to ask the Vermont-based Ben & Jerry’s to stop production of the item, saying the name is nothing but locker room humor that’s not appropriate for young children.

Store chains that have decided not to carry the flavor are not saying whether their decisions were influenced by the One Million Moms group, their own reservations about the name or other factors.

Suzi Robinson, a spokeswoman for the Quincy, Mass.-based Stop & Shop chain, said that for proprietary reasons, the company does not disclose the reasons behind decisions about what the stores do and don’t carry. She said they have a very strong relationship with Ben & Jerry’s, though, and its products are generally strong sellers.

“We haven’t received any complaints that we’re not carrying that flavor. However, if we do get feedback from customers that they want it, we’ll certainly revisit the decision,” she said.

Messages were left Thursday for spokespeople from the Roche Bros. and Big Y grocery chains, both based in Massachusetts; and Publix, which has scores of locations in the southeastern U.S., about whether they had decided to stock the flavor.

Even with limited availability, though, Ben & Jerry’s spokesman Sean Greenwood said Thursday that Schweddy Balls has quickly become the most popular limited-edition flavor the company has produced. Greenwood said about one-third of the retailers that carry its other products are offering Schweddy Balls, about the same as any other specialty flavor it has produced — though this one has outpaced those in sales at the stores and the company’s “Scoop Shops.”

“We’ve heard from lots of folks who are fans of the flavor,” he said. “Yes, some supermarket chains decided not to carry Schweddy Balls. That is true, possibly because they found the name too irreverent. We respect their decision.”

Ben & Jerry’s, a division of consumer products giant Unilever, has toyed with language in some other products, too, such as its widely stocked Karamel Sutra ice cream and the peanut butter-laden What a Cluster, formerly known as Clusterfluff.

But it was Schweddy Balls that raised the ire of the conservative One Million Moms group. Monica Cole, director of the Tupelo, Miss.-based organization, said Thursday they hesitated to call out Ben & Jerry’s publicly about the name because they did not want to give it publicity.

She said they felt obligated, though, especially given that they did not step forward with their concerns about its “Hubby Hubby” flavor, a play on its “Chubby Hubby” flavor and created to recognize same-sex marriages.

“We don’t want the envelope to continue to be pushed,” Cole said of the Schweddy Balls name. “I realize it could be a lot worse, but are they going to progressively get worse if we don’t say something? Maybe they’ll think twice before they come up with another inappropriate name for ice cream.”

The company’s website encourages members and supporters to warn the company they will stop buying its products if more Schweddy Balls or other products with offensive names are produced.

“The vulgar new flavor has turned something as innocent as ice cream into something repulsive. Not exactly what you want a child asking for at the supermarket,” the organization’s website says.

But some are — including Gina Ragusa’s 14-year-old son and 10-year-old daughter, whose mother said Thursday they all eagerly await the day when they can find Schweddy Balls in a supermarket near their home in Davie, Fla. Ragusa, 44, said they find the name and the skit itself to be just harmless humor, and she checks for the item almost every time she stops at her nearby Publix store.

“I get it, I know `Saturday Night Live’ isn’t geared toward a 10-year-old, but they know when Justin Timberlake is on,” said Ragusa, whose family has the “Schweddy balls” skit on a DVD of Baldwin’s greatest SNL appearances.

“We just think it’s funny, that’s all,” she said of the ice cream name, “and honestly we all really want to try it.”